Optical receiver having a maximized signal-to-noise ratio

ABSTRACT

A method of maximizing the signal-to-noise (S/N) ratio or a direct-detecting optical pulse receiver for an input pulse having a well-defined duration and receiver apparatus derived therefrom. The S/N ratio is defined as the ratio of the signal output peak instantaneous power to the noise output mean power. The optical receiver comprises an optical detector with fast-response, highsensitivity characteristics followed by a cascade arrangement of amplifiers, two RC dividing networks, one low pass and the other high pass and an amplitude detector. The noise sources comprise the quantum noise generated within the input light-sensitive device and the thermal noise generated within the input load resistor of the device. The dividing networks form a bandpass filter which is designed to maximize the S/N ratio. As a result, the time constants of the filters turn out to be substantially equal and the output load resistance of the detector is set as high as is practical. The method achieves a S/N ratio approaching that obtainable with an ideal matched filter for small values of the input pulse width (to), e.g., of the order of 10 nanoseconds. The S/N ratio improvement over prior art receivers is in the order of 20 db. The receiver is especially effective when to is less than 1 microsecond.

evr-gu QU LJJ CK Eros et al. 1 1 Apr. 24, 1973 OPTICAL RECEIVER HAVING A Primary Examiner-Albert J. Mayer MAXIMIZED SIGNAL-TO-NOISE Attorney-Hanifin and Jancin and Thomas F. Galvin RATIO [75] Inventors: Stephen Eros, Gaithersburg; Paul M. [57] ABSTRACT Thrasher, Bethe da, borh fMd, A method of maximizing the signal-to-noise (S/N) g ratio or a direct-detecting optical pulse receiver for an [73] Asslgnee' lmemamfnal Busmess Machines input pulse having a well-defined duration and corporamn Al-monk receiver apparatus derived therefrom. The S/N ratio is [22] Filed: Nov. 24, 1970 defined as the ratio of the signal output peak instantaneous power to the noise output mean power. The [211 App! 92'394 optical receiver comprises an optical detector with fast-response, high-sensitivity characteristics followed 52 [1.5. Ci. .250/199, 250/200, 325/323, y a cascade arrangement of p fi t o RC i i 325 477 325 433 325 4 9 329 4 ing networks, one low pass and the other high pass 330/157 and an amplitude detector. The noise sources com- [51] Int. Cl. ..;...H04b 9/00 Prise the quantum noise generated within the Input [58] Field of Search ..250/199, 200, 233, light-Sensitive device and the thermal noise generated 250/833 R, 83.3 H; 329/144; 330/33, 157, within the input load resistor of the device.

180; 324/96 97; 325/323 488-490; The dividing networks form a bandpass filter which is 179/1 Va 15 AA designed to maximize the S/N ratio. As a result, the time constants of the filters turn out to be substantially [56] References cued equal and the output load resistance of the detector is UNn-ED STATES PATENTS set as high as is practical. The method achieves a S/N ratio approaching that obtainable with an ideal 3,286,031 11/1966 I Geddes ..179/1 VC matched filter for small values of the input pulse width 3,646.265 2/1972 Eberhard! (t e.g., of the order of 10 nanoseconds. The S/N 3'470'423 9/1969 Law-w "330/33 ratio improvement over prior art receivers is in the 3,389,34l 6/]968 Thomas ..250/l99 order of The receiver is especially effective when t is less than 1 microsecond.

1 Claim, 8 Drawing Figures 10 ,12 14 16 F I n l AMPLITUDE i I 5' I I DETECTOR I c I I I u *I I I I i I I g I r I I I I 1M5) I I l l I I I Patented April 24, 1973 3 Shuts-Sheet 2 OOQOOQE m QE Patented April 24, 1973 I5 Shuts-Sheet 5 w m m m m m Y W mm X Wm m G F FIG. 5B vousf FIG.5A'

TIME (t) FIG.6B

FIG. 6A

TIME (I) OPTICAL RECEIVER HAVING A MAXIMIZED SIGNAL-TO-NOISE RATIO BACKGROUND OF THE INVENTION receivers has received a great deal of attention in 1 recent years. Many applications depend on the ability of the detector to respond to vanishingly small quantities of radiation which are characterized by low current levels and short pulse widths. This is particularly important in the fields of optical communication, optical instrumentation and Raman spectroscopy.

Prior to the present invention, the principal means used to detect optical pulses were direct-detection optical receivers or heterodyne-type optical communication receivers. The heterodyne receiver has been recognized as more noise-immune than the direct-detection receiver; on the other hand, the heterodyne receiver is quite a bit more complex. As a result, the direct-detection optical receiver is usually to be preferred over a heterodyne receiver. However, the S/N ratio of the input light pulses in direct-detecting receivers remains a significant problem. Furthermore, this problem worsens as the ability to generate coherent pulses of very short duration improves. See, for example, the article on Optical Receivers by V. K. Prabhu in Applied Optics, Vol. 7, No. l2, pp 2,401-08, December 1968.

For a maximum S/N ratio in direct-detecting receivers, it is well known that t the duration of the input pulse, should be equal to 1.26 RC, where RC is the time constant of the receiver. If t becomes smaller, then the bandwidth of the receiver must increase and either R or C must be decreased. But C is usually limited by the capacitance of the photodetector and other system capacitances. The latest semiconductor detectors, for example, have a minimum capacitance in the order of picofarads, primarily due to the junction capacitance.

Because of the fixed capacitance (C), the load resistance (R) of the detector must be reduced if the bandwidth is to be increased. However, the S/N ratio of a receiver having a large bandwidth is generally proportional to R; and the S/N ratio is correspondingly reduced as R is reduced. In the past, when relatively long pulses were standard, a high S/N ratio was ensured merely by adhering to the criterion t 1.26 RC, allowed R to be set large enough. However, as already explained, the advent of shorter duration input pulses requires R to be small in receivers designed for optical detection. Designers in this field have been unable to solve this dilemma.

SUMMARY OF THE INVENTION It is therefore an object of this invention to improve the detection ofoptical pulses.

It is a further object of this invention to detect optical pulses having very narrow pulse widths by an apparatus which is less expensive and more practical than prior art receivers.

It is another object of this invention to improve the signal-to-noise ratio of a laser receiver.

0 perature of the photodetector. R is thereby made large These and other objects are achieved in a laser receiver basically comprising a direct-detecting photodetector and a bandpass filter connected to its output. The load resistance, R of the detector is designed to be large enough to substantially maximize the term (R /I eR ZkT), where 1,, is the DC. current through the photodetector, e is the charge on the electron, k is Boltzmans constant and Tis the absolute temespecially for small values of I,,; and the photodetector itself is a low-pass filter.

The bandpass filter comprises a low-pass and highpass filter in cascade. The filters are constructed so that their time constants are substantially equal to each other and designed to maximize the signal-to-noise relationship:

where: A is the amplitude of the input optical current pulse; 1 e, R,, k and T are as previously defined; a, B and y are the time constants of the photodetector, and the highand low-pass filters of the bandpass filter, respectively; and r is the time at which the output signal is at its maximum. It turns out that 1,, equals t for the great majority of cases and that I t 5 1,, for all cases.

Equation 1 is the result of a process to describe the S/N ratio in terms of the receiver parameters. It is derived from the basic relationship:

(2) q/N (|)('2l.k signal output voltutus) output. Iottd resistance output noise power The procedure for determining the values of R and the time constants, B and -y, of the bandpass filter is. as follows.

First, an equation for the peak value of the output signal voltage, termed v,,(max), is determined and inserted in the numerator of equation 2. Second, equations for the output noise power of the receiver, which consists of the thermal and quantum noise, are determined and inserted in the denominator of equation 2. This establishes equation 1. The output load resistance is assumed to be 1 ohm, for ease of computation.

Analysis of equation l indicates that the S/N ratio is maximized when R is selected to substantially maximize the term (R /l e'R 2kT) and when the time constants of the low-pass and high-pass filters of the bandpass filter are set equal and selected to maximize the equation.

Compared with direct-detecting receivers having only a post-detection, low-pass filter to limit amplifier noise, the S/N ratio of the inventive receiver is substantially improved, as will be demonstrated.

BRIEF DESCRIPTION OF THE DRAWINGS nection with the accompanying drawings, forming a part thereof, in which:

FIG. 1 is a schematic drawing of the optical receiver of the present invention.

FIG. 2 is a graph of the output voltage of the receiver in FIG. 1 versus time for a given input pulse width, 1,.

FIG. 3 is a graph of the term (R,/l,,eR, 2kT) of equation 1 versus R, for various values ofl,,.

FIG. 4 shows the transfer functions of the: individual components and of the overall receiver of the present invention.

FIGS. 5 and 6 are tracings of oscilloscope patterns of output signals which illustrate the improved results of the inventive direct-detecting receiver over the prior art receiver.

Referring now to FIG. 1, there is shown the equivalent circuit of the optical receiver of the present invention. The input light-sensitive device takes the equivalent form of capacitor C, and resistor R, fed by a current source denoted as l,,,(s). The capacitor C, represents 'the junction capacitance of the device plus any shunting capacitances. The resistor R, is the load resistance of the device shunted by the very high junction resistance of the device. For practical purposes R, is regarded as the load resistance alone. This type of equivalent circuit is well known to those of skill in the art as representing standard light-sensitive devices. For example, device 10 may be a small area, silicon photodiode. Input current pulse 8 has a duration of t seconds.

The output of device 10 is connected to amplifier A,. The output of amplifier A, is connected to voltage divider 12 which consists of a RC circuit where the capacitance is denoted as C, and the resistance is denoted as R As will be completely described later, divider 12 is a high-pass filter. The output of filter 12 is connected to amplifier A The output of amplifier A is connected to voltage divider 14 which consists of capacitor C and resistor R Divider 14 is a low-pass filter whose characteristics will also be described later. The output of divider 14 is connected to amplifier A The output of amplifier A is connected to a standard amplitude detector 16.

Each of amplifiers A A and A shown in FIG. I have high-input impedance, low-output impedance, a flat frequency response and gain factors K,,, K and K,-, respectively. The noise contributed by the amplifiers is assumed to be negligible. Even in the presence of significant amplifier noise, however, the inventive method will yield a substantial improvement in S/N ratio for small pulse widths. In the present circuit the characteristics as outlined for the amplifiers insure that their inputs do not load the preceding circuit; their outputs act as voltage sources; the overall frequency characteristics are determined by the specific R and C elements of circuits l0, l2 and 14; and the only noise sources are those due to the input circuit to the first amplifier, i.e., device 10.

The transfer functions in Laplace Transform notation of each of the components of FIG. 1 are easily calculated by those of skill in the art and the calculations will not be described here. For example, the transfer function, H,(s), of the device 10 equals and the Laplace Transform of the input signal, I,,,, equals f tl l.

Peak Value of the Output Voltage In the circuit shown in FIG. 1, the output voltage V is, by standard linear network analysis:

Substituting for l,,, (5), equation 3 then becomes:

KAKB Q; 51 lflihJ- /L GIGS/)1 [S -][S Ml w][q+r l mc, rac 1: 0,

The inverse transform of V,,(s) in equation 5 is:

where, for notational convenience, the time constants of device 10 and dividers l2 and 14 of FIG. 1 are denoted as follows:

The maximum value of equation 6, termedv,,(max), is to be used in the numerator of equation 2. Because only this maximum value of v, (t) is desired, equation 5 can be further simplified by noting that 1, the time at which v,,(max) occurs, must always be l,,. Hence, the last three terms in equation 6 are not required to determine v,,(max). To see this, first note that at l 1,, the last three terms vanish because I r and t each equal one for i=1, and the terms a(,B-y) B(a 'y) y(a-B) then cancel each other. Second, at! the last three terms vanish because U(tt,,) o for l l Finally, for r t,,, equation 6 can be considered to consist of two parts, the first three terms and the second three terms. The second three terms represent a 6 function that is a duplicate of that represented by the The input RMS quantum or shot noise current, I first three, but opposite in polarity and shifted to the may b expresse in terms of the well-known formula right by 1,. This may be seen in FIG. 2 which is a graph stated, e.g., in the textbook, Noise, A. Van der Ziel, of the output voltage v, versus time for equation 6. The Prentice-Hall, 95 a o lo s: input pulse duration in this example is selected to be 5 01v V o f nanoseconds and the values of the other parameters are Where: arbitrarily selected. The portions of the curves shown 0 is the average Current, by dotted lines on the positive and negative side of the t is the Charge the electron, axis represent positive and negative step function the Subscript Q denotes quantum noise, responses, respectively, to the input signal. The positive 10 and f the bandwidth o he Signal. response in H6. 2 is due to the first three terms of lh this case, 0 is a function of the background noise, equation 6; i i counteracted, after to, b h negathe D.C. component of the signal and the dark current tive response hi h i d to h l three terms f of the photodiode. The spectral distribution for this e uati n 6, Th f t l output i d d b a heavy li input current is white. To develop the expression for and the maximum output voltage in this example octhe Output quantum noise P We begin with the curs pr ci el at z= r previously stated equation for output voltage, equation 3, and express it in terms of (jw) for (s) and l for I Therefore, it may be seen from FIG. 2 that v (t) is Equation 3 then becomes:

( l 7 J j i+ @1r,c, i+ wlz cn i+ wlncn monotonically decreasing at t and v,,(t t must al- The total output quantum-noise power, P assuming ways be less than v (t So, v,,(max) can occur only for that this voltage is delivered to a 19 load, becomes:

values of z 5 t and the last three terms of equation 6 M ltiplying the integrand through by complex conjucan be ignored when c l ul i E i 6 i gate factors for each of the denominator factors in the then simplified a d w i integrand, and separating into real and imaginary parts:

where; K]: KAKBKCRIRZCZ; K2 R c RzcgRaca; K3 R1C1+ Rzcz Raca; and K4 RICIRZCQ R1C1R3C3 'l' UQ(III2LX) R C ab3C Equation 1 1 becomes:

[r..u 40 l 5 (l2 =A-]\,\l\l;l\ (I; (lx fi)(a f)(fi X(li"')l; I) ?-IUI,I-KZ[KE [m e (IQ w l) (l)|CI\'0;\4)'- [1(01 ()0 I ((0: Mt. +(1\ .Zh hflfn J AU rZw r I U. 4 v u where 5 Mull it, (DEN! l \l .lu uncxoM P Equation 7 is the expression that is to be used in the numerator of the S/N ratio given in equation 2. Where DENOM 2 2 n a It will be noted that equation 7 is indeterminate at a q t on 12 must be evaluated. The right-hand side in- B, a y or B 7. However, application of LHopitals VOlVeS an egr o the general form: Rule indicates that the function is continuous for these values. (13) In the great majority of practical cases, v,,(max) ocm l curs precisely at l t,,, i.e., t,,,,,,= t However, for input i \'2 2 i z 2 a -1 1 pulses of long duration, v may occur at some value of r t,,. A procedure for determining I is where n 2, 4, 6, 8. described in a later section of this specification. An integral of this form may be evaluated by residues Output Noise Power using conventional contour integration techniques. To

1. Quantum Noise use this method integral 13 is written in the form:

7 8 The integral is considered to be a function of a comcase. It may readily be seen that when this is done the plex variable and is evaluated around a semi-circle, exfinal result is:

tending from to R, then to R along the semi-circle (19) and back to zero, with R being allowed to go to This "m=% integral is set equal to 21ri multiplied by the sum of the 5 7 7 residues. Because, for n 2, 4, 6, 8, the function is This is the expression for the thermal noise portion of even,the integral may be written as: the denominator of the overall S/N ratio defined in equation 2. Overall S/N Ratio 1" dz 10 The equations calculated in Steps I and [l for 0 2 1 2+ 1 2+ 1 v,(max), P and P are now inserted into equation 2 (MCI,l2 (R202) (R3092 to obtain the following overall result:

21:. (a -l worm/1+7) I: w W: 1 M l ,l"li'.rl 2kl' (or /1 *(a--v)(fiv) a 7) H Wm M I 7 :l

=21ri2 residues. where: 1, 5 t and the output load resistance is The term 21ri 2 residues is to be evaluated, where the 20 assumed to be 1 ohm. This is the relationship to be poles enclosed by the contour are: 2 (i/R C Z, maximized. (i/R C and Z (ilR C Design Steps for the Receiver This evaluation is done for each value of n, with x set Step I equal to to. Equation 12 reduces to: Inspection of equation 20 leads to the first step in ob- 25 taining the maximum value of the S/N ratio. In particular, the S/N ratio is dependent on the term: (R R (16) 2kT). It will increase asymptotically as R 1 increases and .will decrease as l increases. The values of e and k are, Q of course, physical constants and T is constant for a given application. Therefore, the S/N value due only to 1 I K12 2 the tenn (R,/I,,eR 2kT) is essentially a function of K756 17562WRIGH 6 1it REA 1?; at R, only.

FIG. 3 is a plot of the term (R,/I,,e'R 2kT) versus The above equation may be written in simpler form R, for values of 1. from 10' to 10' amperes. For these as: values of 1,, it may be seen that the term increases until (17) s jK KnKo ffiV it reaches an asymptote; i.e., an increase in R causes 2 (a+B) (0+7) (5+1) the term to increase until R reaches a certain value where as previously noted a: RCIB Rzcz and y after which the term remains essentially constant. The Racy 40 value of R, which maxlmizes the term depends on 1,. This is the expression for the quantum-noise power For m 3 for the term portion of the denominator of the overall S/N ratio 2kT) become,s asympt9lc at around 8 which is to be maximized 10 ohms. Any further increase in R, results in a Thermal Noise negligible increase in the term. Therefore, in equation The determination of the expression for the thermalf Object is to choose R1 to have at least the value noise power is similar to that of the quantum-noise at Yvhlch the term (RI/IOEIRI 2kT) becomes asymppower. The only difference in the process is a maniputone or In: 104 amperes, R1 Ohms: lation of the equivalent input circuit to make it like that Havmg fixed the value q l 20 also used for the quantum-noise and signal inputs. The therfixed f 1 and Ch P capacltance of the mall noise is that generated in the resistor R1 of FIG detector, IS a function of the particular detector used.

The usual equivalent circuit for this type of noise, as Step 1 given in Information Transmission, Modulation and The f step m h maxlmlzanon process "wolves Noise Schwartz McGrawHm' 1959 is a voltage the deslgn of the optimum values offi and 7, the bandsource with a RMS value as follows: w'dth-dewrmmmg factors- To carry out this calculation, it IS convenient to turn 8 1-= V 4 l f to computerized computations. Equation 20 has been where: k is the Boltzman constant, T is the absolute exammed for max'mum S/N by varymg B F 7 temperature, the subscript TN denotes thermal noise h other f fixed The pmgramwmg for and Afis the Signal bandwidth kind of analysis IS simple, and may be carried out con- This voltage is in series with the resistor, R,, generat- 'l almost computer d esigned 9 ing the noise. By using Norton's theorem, this is scientific type calculations. The programming for this changed to a current source with a value equal to application has been carried out in the APL/36O V (4kT/R|Afin parallel with R|. Thus, the circuit to be language- This is a know" Programming language utilized in determining the output thermal-noise power and is explained in y Mil/360 is FIG. 1, with this value of input current. The spectral IBM Technical Publications- 1969- Computations y distribution for this type of noise is white. Thus, for this be carried out with an APL/360 lermmal- Cas simp y Substitute 1) f uv) in This kind of analysis indicates that equation 20 alstead of o f as was done the quantum-noise ways reaches a near maximum at a point on the line B 9 ll) 3!. Therefore, equation 20 can be further simplified by time constant of the input filter R,C,. allowingB=-y. FIGS. 5 and 6 are oscilloscope traces of the output 'B and Y, equation 20 becomes! pulses from a conventional photodetector receiver of where t 5 t,,. the prior art and from the photodetector incorporating It will be noted that there is an indeterminancy in 10 the bandpass filter of the present invention. In both equation for [3 y. However, by applying L- figures the input pulse width, t is 100 nanoseconds Hopitals Rule it is found that equation 20 is in fact and the same input amplifier (A, of FIG. 1) is emcontinuous atB='y. ployed. Thus, the input amplifier noise is the same for Conceptually, the calculations involved in computb h cases, Thi am lifier has only a moderately low ing the values ofB (hence y) to maximize equation 2] l5 noise voltage. are straightforward. Initially, the value of 1,, I, is Output pulses for the conventional receiver are illusspecified. In this invention, as noted previously, the trated in FIGS. 5A and 6A; output pulses for the value of t is assumed to be known precisely. Similarly, receiver of this invention are illustrated in FIGS. 53

the value of I, is fixed, depending on the particular type and 6B. of detector used and the input signal characteristics. 20 For the conventional photodetector receiver, low- Then, the values of R, and a are designed as described pass post-detection filtering is used to limit the amplifiin Step I above. er noise. The bandwidth of this filtering is sufficient so Having specified the values of t I,,, and having as not to limit the bandwidth required for the signal, as designed R, and a, the value ofB which maximizes S/N determined by the conventional or time constant (a in equation 2l is determined by performing clacula- 0.794 t tions for S/N over a series of values of 3. The pro- In FIG. 5, the amplitude of the input pulse is set at a gramming involved in this step is quite simple. high value, thereby making the input S/N high. This is As previously noted, in the great majority of practidone in order to facilitate the comparison of the output Cal cases, the Value of mfl: is precisely o, the inp signal waveforms. It may be seen that the waveforms pulse width. However, this is not necessarily the case, are almost alike, indicating that the "effective time as there may be a value of t lying between 0 and t constant" of the overall circuit for the present invenwhich is in fact I A procedure for determining the tion (FIG. 5B) is nearly that for the conventional detecvalue of 2,, is to assume initially that I =1, in equator (FIG. 5A). This occurs even though a for the invention (21). Then, solve equation 21 for [3, all other tive receiver has been made much larger than a parameters having been specified. Having found the 0.794 t in order to improve the S/N ratio. Thus, even numerical value ofB which maximizes equation 2 l this though the fast response of the detector is destroyed at value is substituted in equation 7 for B and 7. All other the input by increasing R, in order to improve the S/N parameters on the right hand side of equation 7 are alratio, the overall effect is that the response is recovered ready known, except r Equation 7 is then solved for by the proper choice ofB=-y. values oft 5 z, and v,,(max) is determined which oc- In FIG. 6. the inpu S/N h a low l e an emoncurs at a particular value of 2, which is I This step is strates the improvement in S/N ratio. The signal-toeasily done by a suitable computer program. In the noise improvement of the signal in FIG. 68 compared usual case, i.e., when r t the maximum value of with the signal in FIG. 6A is 10.4 db. If no amplifier S/N remains as calculated from equation 2i. In the rare noise were present the improvement would be even case where r is some value oft t;,, a new value ofB greater, approaching the ideal level of a matched filter. which maximizes equation 21 is computed. For shorter pulse widths, the increase in S/N ratio FIG. 4 illustrates typical absolute values of the power becomes even greater. This has great significance for transfer functions for the component parts of the future applications, since as the capability of handling receiver of FIG. 1 and the resulting overall transfer shorter pulses increases, this technique will become function designed according to the present invention. more applicable. In this particular desi n, the duration of the in ut ulse, l,, is 100 nanosecond? The detector charactefistiss are SUMMARY OF THE DETAILED DESCRIPTION Such that l is 20 Plcofarads and 0 is P There are three basic design parameters that in the Using the design procedure described above, R, is 3 usual case serve to define the problem. These are: input kllohms and B and 7 are 3i X StlCOndS- I! Will be pulse width 1,, the capacity, C,., of the input low-pass seen that photodetector I0 has a low-pass charac i i 10 d h DC current, h h h teristic with a relatively low 3 db roll-off frequency due photodetector. to the high value of R,. Filters 12 and 14 have high-pass 0 The value of 1,, must be known prior to the design and low-pass characteristics, respectively, with their 3 procedure. For the usual laser receiver, t will be less db points intersecting at 5.14 X l0 Hz. The overall than I00 nanoseconds. C, is fixed by the choice of characteristic is bandpass. photodetector and its biasing, the input capacitance of In operation, the optical pulse detected by detector he fi t lifi r A a d th capacity of the input 10 is passe thro gh th low-p ss filt r RI ng a cabling from the detector to the amplifier. It is desiralarge time constant a. The detected pulse is then passed ble to make C, as small as possible but, in practice, this through the bandpass filter (filters l2 and I4) comprisminimum value will be of the order of 10 to 20 pf. l is ing R,C, and R C which compensates for the large the factor on which the quantum noise depends and is a function of the dark current, background noise and DC. component of the detected signal pulse. It has been pointed out that I should be as small as possible; values for 1,, of less than 10' amperes are achievable.

With 1,, C, and I, specified, the first step in the procedure is to determine R,, which specifies a, the input time constant. In the conventional approach, R, is fixed by the maximizing relationship R,C, 0.794 2,. However, for small values of 1,, and a fixed minimum value of C,, this results in a R, so small that the term (R,/I,,eR, 2kT) does not approach its limit of l/I,,e' This results in an output S/N ratio that can be many db below that of a matched filter. In the present invention, on the other hand, R, is made large enough to cause the term (R ll e'R, 2kT) to approach its limit. In practical cases, it may not be possible to make R, physically as large as desired. However, the concept remains the same, and in these instances R, is made as large as possible.

Having established the value of R,, a R,C, is fixed thereby. The input low-pass circuit 10 of FIG. 1 is thus a low-pass filter with a 3 db cut-off radian frequency point, w much lower in frequency than for the conventional case, because m (1/0!) (l/R,C,) and R, has become much larger. In addition. the low-pass transfer function, H (iw) (R,/l +jwR,C,), has increased in amplitude because of the increase in R,. Hence, the effect of increasing a for the present invention is to move the 3 db cut-off radian frequency point in toward a lower frequency, but at the same time to increase its amplitude over prior-art detectors.

With 1,, C,, 1 R, and a fixed, the next step is to determine the time constants B and y for the cascaded high-pass and low-pass dividers, 12 and 14, respectively. B(R C always equals 'y(R C as determined from the mathematical maximization calculation in equation 20. The specific values of B and y are then calculated by solving equation 20 for various values of B and y until those values which maximize the equation are obtained. As has been pointed out, the calculations are tedious and, in practical cases, must be done with the aid of a computer. However, the programming is simple and there are many computers capable of doing the calculations. This completes the procedure.

The apparatus which results from the above design procedure is a high-pass divider 12 and a low-pass divider 14 which, in cascade, produce a bandpass filter having a peak at a frequency of wa w.-,. This bandpass filter in cascade with the input low-pass filter produces an overall transfer function that is bandpass. Its characteristics are similar to the low-pass transfer function for the conventional detector which has the condition a 0.794 t imposed. Thus, the bandpass technique produces an overall transfer function that is about equivalent to that produced by the conventional approach, but achieves this with a larger value of R,,

which accounts for the significant increase in output S/N ratio at amplitude detector 16. Note that it is required only that B and 'y substantially equal a certain value; one is free to choose R C R,, and C, as desired, subject only to the constraint that the products R C and R C be as specified.

In the preferred embodiment of FIG. 1, three amplifiers A,, A and A are used, which are considered to be ideal from the viewpoint of input and output impedance, frequency response and noise; but it has been pointed out that the input impedance of A, forms a part of the input RC circuit. This input impedance could very well be the limiting factor in determining how small C, and how large R, can be made. In practice, A and A, could be eliminated. A, would have to be of the low-noise variety. At the output of amplifier A,, the frequency characteristics of the cascaded high-pass and low-pass dividers could be combined. This means that the amplifier would be peaked at 0: w as defined above.

While the invention has been particularly shown and described with reference to a preferred embodiment thereof, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention. For example, the bandpass filters shown in FIG. 1 are preferably composed of resistances and capacitances. However, it is obvious that various combinations using inductances as well could be used.

What is claimed is:

l. A method for constructing a direct detecting optical pulse receiver having an optical detector with a load resistance R,, a junction capacitance plus shunt capacitance C,, and a time constant at equal to R, C,, a high-pass filter with a time instant B and a low-pass filter with a time constant 7, said high-pass and lowpass filters being connected in cascade to the output of said optical detector, comprising the steps of:

setting said resistance R, to a value which makes the term (R,/l,,,eR, 2kT) substantially equal to l/l,,e where I,, is the DC. current of the detector, e is the charge on the electron, k is Boltzmanns constant and T is the temperature of the detector;

setting the time constants B and y equal to each other at a value which substantially maximizes the relationship: where S/N is the signal-to-noise ratio and is defined as the peak signal output voltage squared divided by the output load resistance of the receiver, A is the amplitude of the input optical current pulse and 1,, is the time at which the peak signal output voltage occurs,

whereby the signal-to-noise ratio of the optical receiver is maximized.

my I UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION 3,729, 633 April 24, 1973 Patent No. Dated Inventor(s) Stephen Eros and Paul M. Thrasher It is certified that error appears in the above-identified patent andthat said Letters Patent are hereby corrected as shown below:

Column 6 (1 1) line 39, "R C ab3C should read --R C R C Column 8, line 26, (R /I. R 'should read (R /I g R1+ Lines 52-54 should precede Equation (21) Signed and sealed this 7th day of January 1.975.

(SEAL).

Attest:

McCOY M. GIBSON JR. C. MARSHALL DANN Arresting Officer Commissioner of Patents 

1. A method for constructing a direct detecting optical pulse receiver having an optical detector with a load resistance R1, a junction capacitance plus shunt capacitance C1, and a time constant Alpha equal to R1 C1, a high-pass filter with a time instant Beta and a low-pass filter with a time constant gamma , said high-pass and low-pass filters being connected in cascade to the output of said optical detector, comprising the steps of: setting said resistance R1 to a value which makes the term (R1/IIoe''R1 + 2kT) substantially equal to 1/Ioe'', where Io is the D.C. current of the detector, e'' is the charge on the electron, k is Boltzmann''s constant and T is the temperature of the detector; setting the time constants Beta and gamma equal to each other at a value which substantially maximizes the relationship: 